A Bidimensional Stability Result for Aluminum Electrolytic Cells

This paper shows that the instabilities which are observed in cells cannot be explained by supposing that the mechanical and electromagnetic fields are independent of the space variable x3 corresponding to the length of the cell. For a model which is infinitely long in the x3-direction, we prove in particular that the kinetic energy due to the x1- and x2-components of the velocities tends to zero as the time tends to infinity.